Pro-C group

In mathematics, more precisely in the areas of algebra and group theory , a pro group denotes the inverse or projective limit of an inverse system of groups, which can be any category of groups. ${\displaystyle {C}}$ ${\displaystyle {C}}$ ${\displaystyle {C}}$

Examples

• If the groups occurring in the inverse system are finite (more rarely also called finite ), one speaks of a profinite (less often: pro-finite ) group.
• If the groups occurring in the inverse system are cyclic , one speaks of a procyclic group.
• Are occurring in the inverse system groups Abelian , then one speaks of a pro-Abelian group.
• If the groups occurring in the inverse system are resolvable , one speaks of a pro-resolvable group .